{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2,  2, -8, -6, -4,  6,  1, -6,  4,  8])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nums = np.random.randint(-9, 9, (10,))\n",
    "nums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def algorithm(nums, target):\n",
    "    n = len(nums)\n",
    "    nums.sort()      # 指针使用标准操作：排序\n",
    "    result = []\n",
    "    \n",
    "    move = []     # 可视化记录列表\n",
    "    for i in range(n):    # i指针代表第一个数\n",
    "        if i>0 and nums[i]==nums[i-1]:       # i>0是因为数列第一个不需去重，与i-1比较代表去重是去已经出现过的元素\n",
    "            continue\n",
    "        if nums[i]>target and nums[i]>0 and target>0:   # 剪枝：只有都大于0时可以考虑剪枝，因为当第一个数都大于0且大于target（排序代表后续值都大于当前值大于0），此时继续加肯定找不到四数和满足要求\n",
    "            break\n",
    "        for j in range(i+1, n):     # j指针代表第二个数，从i的下一个数开始遍历\n",
    "            if j >i+1 and nums[j]==nums[j-1]:   # j>i+1也是因为遍历第一个数不需去重\n",
    "                continue\n",
    "            if nums[i]+nums[j]>target and target>0:    # 剪枝：同样只有大于0考虑，第一个数已经判断过大于0，此时因为顺序排序，j指向的第二个数肯定大于0，现在只需保证target大于0，即可判断\n",
    "                break\n",
    "            left = j+1     \n",
    "            right = n-1        # 设置左右指针来选择最后两个数。对于更多数之和，此处不变，只需将前面遍历增加指针\n",
    "            while left<right:\n",
    "                move.append((i,j,left,right))\n",
    "                \n",
    "                s = nums[i]+nums[j]+nums[left]+nums[right]\n",
    "                if s==target:\n",
    "                    result.append([nums[i],nums[j],nums[left],nums[right]])\n",
    "                    while left<right and nums[left]==nums[left+1]:  # 去重。此处需判断left<right是为了防止当left和right对应数相等时，去重操作会使左右指针指向同一个数。判断是当前和+1后相等，就跳过下一个\n",
    "                        left +=1                                    # 左侧去重看下一个，因为左指针向右移动\n",
    "                    while left<right and nums[right]==nums[right-1]:  # 右侧去重看上一个，因为右指针向左移动\n",
    "                        right -=1\n",
    "                    left +=1\n",
    "                    right -=1  # 将保持的指针数跳过\n",
    "                elif s<target:\n",
    "                    left +=1\n",
    "                else:\n",
    "                    right -=1\n",
    "    return result,move"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[-8, 1, 2, 6], [-6, -2, 1, 8], [-6, 1, 2, 4], [-4, -2, 1, 6]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result,move = algorithm(nums, target=1)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#指针移动可视化\n",
    "def visualize_pointer_movement_with_squares(nums,move):\n",
    "    nums.sort()\n",
    "    original_nums = nums.copy()\n",
    "    pointer_movements = move\n",
    "    fig, ax = plt.subplots(figsize=(12, 4))\n",
    "    \n",
    "    for i, num in enumerate(original_nums):\n",
    "        ax.text(i, 0.5, num, ha='center', va='center', fontsize=12)\n",
    "        ax.add_patch(plt.Rectangle((i - 0.5, 0), 1, 1, fill=None, edgecolor='black'))\n",
    "\n",
    "    start_pointer, = ax.plot([], [], 'r^', label='Start Pointer', markersize=10)\n",
    "    start2_pointer, = ax.plot([], [], 'bv', label='Start2 Pointer', markersize=10)\n",
    "    fast_pointer, = ax.plot([], [], 'r^', label='Fast Pointer', markersize=10)\n",
    "    slow_pointer, = ax.plot([], [], 'bv', label='Slow Pointer', markersize=10)\n",
    "    ax.set_xlim(-0.5, len(nums) - 0.5)\n",
    "    ax.set_ylim(-1, 2)\n",
    "    ax.axis('off')\n",
    "    ax.legend(loc='upper right')\n",
    "\n",
    "    def update(frame):\n",
    "        start, start2, fast, slow = pointer_movements[frame]\n",
    "        start_pointer.set_data((start , ),(-0.5,))\n",
    "        start2_pointer.set_data((start2 , ),(1.5,))\n",
    "        fast_pointer.set_data((fast ,), (1.5,))\n",
    "        slow_pointer.set_data((slow ,), (-0.5,))\n",
    "        return fast_pointer, slow_pointer\n",
    "\n",
    "    ani = animation.FuncAnimation(fig, update, frames=len(pointer_movements), interval=800, blit=True)\n",
    "    return HTML(ani.to_jshtml())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img3222cae8837e44dfa06701a630676134\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider3222cae8837e44dfa06701a630676134\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim3222cae8837e44dfa06701a630676134.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" onclick=\"anim3222cae8837e44dfa06701a630676134.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" onclick=\"anim3222cae8837e44dfa06701a630676134.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" onclick=\"anim3222cae8837e44dfa06701a630676134.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" onclick=\"anim3222cae8837e44dfa06701a630676134.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" onclick=\"anim3222cae8837e44dfa06701a630676134.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" onclick=\"anim3222cae8837e44dfa06701a630676134.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" onclick=\"anim3222cae8837e44dfa06701a630676134.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" onclick=\"anim3222cae8837e44dfa06701a630676134.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" onclick=\"anim3222cae8837e44dfa06701a630676134.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select3222cae8837e44dfa06701a630676134\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_3222cae8837e44dfa06701a630676134\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_3222cae8837e44dfa06701a630676134\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_3222cae8837e44dfa06701a630676134\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_3222cae8837e44dfa06701a630676134\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_3222cae8837e44dfa06701a630676134\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_3222cae8837e44dfa06701a630676134\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img3222cae8837e44dfa06701a630676134\";\n",
       "    var slider_id = \"_anim_slider3222cae8837e44dfa06701a630676134\";\n",
       "    var loop_select_id = \"_anim_loop_select3222cae8837e44dfa06701a630676134\";\n",
       "    var frames = new Array(55);\n",
       "    \n",
       "  frames[0] = \"\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim3222cae8837e44dfa06701a630676134 = new Animation(frames, img_id, slider_id, 800.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_pointer_movement_with_squares(nums, move)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
